Application of Dimension Extending Technique to Unified Hardening Model
This paper provides the process of incremental constitutive integration for the unified hardening model combined with the transformation stress method. The dimension-extending technique takes the hardening function of the hardening/softening model as the same position as the stress components, so th...
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| Vydáno v: | Applied sciences Ročník 14; číslo 13; s. 5677 |
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MDPI AG
01.07.2024
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| ISSN: | 2076-3417, 2076-3417 |
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| Abstract | This paper provides the process of incremental constitutive integration for the unified hardening model combined with the transformation stress method. The dimension-extending technique takes the hardening function of the hardening/softening model as the same position as the stress components, so that the constitutive integration of the plasticity can be reduced to an initial value problem of differential–complementarity equations, which is solved using the Gauss–Seidel algorithm-based Projection–Correction for the mixed complementarity problem. The Gauss–Seidel based Projection–Correction algorithm does not require the calculation of the Jacobean matrix of the potential function, making it relatively easy to implement in programming. The unified hardening model is proposed based on the modified Cam–Clay model and the sub-loading surface model, and the elastic properties are pressure-dependent. Two processing methods, backward Euler integration and exact elastic property, are used for the variable elasticity properties. The constitutive integration of the increased dimensional unified hardening model is reduced to a special mixed complementarity problem and solved by the proposed algorithm, which does not need to calculate the Jacobean matrix of the potential function, and greatly simplifies the derivation process. Several numerical examples are given to verify the feasibility of the incremental constitutive integration in the unified hardening model, including the single integral point and the boundary value problems. The research results have expanded the scope of use of the Gauss–Seidel based Projection–Correction algorithm. |
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| AbstractList | This paper provides the process of incremental constitutive integration for the unified hardening model combined with the transformation stress method. The dimension-extending technique takes the hardening function of the hardening/softening model as the same position as the stress components, so that the constitutive integration of the plasticity can be reduced to an initial value problem of differential–complementarity equations, which is solved using the Gauss–Seidel algorithm-based Projection–Correction for the mixed complementarity problem. The Gauss–Seidel based Projection–Correction algorithm does not require the calculation of the Jacobean matrix of the potential function, making it relatively easy to implement in programming. The unified hardening model is proposed based on the modified Cam–Clay model and the sub-loading surface model, and the elastic properties are pressure-dependent. Two processing methods, backward Euler integration and exact elastic property, are used for the variable elasticity properties. The constitutive integration of the increased dimensional unified hardening model is reduced to a special mixed complementarity problem and solved by the proposed algorithm, which does not need to calculate the Jacobean matrix of the potential function, and greatly simplifies the derivation process. Several numerical examples are given to verify the feasibility of the incremental constitutive integration in the unified hardening model, including the single integral point and the boundary value problems. The research results have expanded the scope of use of the Gauss–Seidel based Projection–Correction algorithm. |
| Author | Tian, Dongshuai Zheng, Hong Chen, Qian |
| Author_xml | – sequence: 1 givenname: Qian surname: Chen fullname: Chen, Qian – sequence: 2 givenname: Hong surname: Zheng fullname: Zheng, Hong – sequence: 3 givenname: Dongshuai surname: Tian fullname: Tian, Dongshuai |
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| Cites_doi | 10.1061/(ASCE)0733-9399(1986)112:9(966) 10.1007/b97543 10.1007/s004660000166 10.1061/(ASCE)0733-9399(2009)135:4(276) 10.1016/0045-7825(90)90152-C 10.3390/app13095746 10.1061/(ASCE)0733-9399(2000)126:1(112) 10.1016/j.cma.2022.114833 10.1016/0020-7683(77)90073-7 10.3208/sandf.39.81 10.3208/sandf.44.2_53 10.1002/nme.1620230303 10.1061/(ASCE)EM.1943-7889.0000685 10.1007/s002459900037 10.1007/978-1-4419-6379-6 10.1016/j.compgeo.2021.104064 10.1016/0045-7825(85)90070-2 10.1017/CBO9781139878272 10.1002/(SICI)1099-1484(199601)1:1<75::AID-CFM4>3.0.CO;2-I 10.1016/0045-7825(85)90061-1 10.1016/j.cma.2019.112756 10.1680/geot.2007.00029 10.1061/40771(169)14 |
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| SubjectTerms | Accuracy Algorithms backward Euler integration constitutive integration dimension-extending technique Gauss–Seidel based Projection–Correction mixed complementarity problem Numerical analysis Ordinary differential equations unified hardening model |
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| Title | Application of Dimension Extending Technique to Unified Hardening Model |
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